Exercise 1.20. Show that the series 7t 12 +22m-52 32z-10m2 converges absolutely for |2l< 1
Exercise 3. Suppose that |2 < 2. Prove that the series converges absolutely.
bn converges 18. Let (an)n=1 and (bn)n=1 be sequences in R. Show that if and lan – an+1 < oo, then anbr converges.
HW: Show that the series __, an n=0 converges whenever ſal < 1, and diverges whenever al > 0.
For the series <1-1n in n +1 n=1 1. Does it converge? 2. Does it absolutely converge? Please present your work in 1 pdf file with 2 pages (ONE subproblem per page)
Show that a bounded and monotone sequence converges. Here a sequence is called monotone, if it is either monotone increasing, that is for all or monotone decreasing, in which case for all . in Sn=1 An+1 > an neN an+1 < an We were unable to transcribe this image
2. Determine and sketch the spectrum, the Fourier transform, of x() where -2l +cos(0)+ jsin for -<t<
please include the graph 1. Expand 7T if 0 <<< f(x) = 1 if <<, in a half-range: (a) Sine series. (b) Cosine series.
7T TT 1. Show that < 1 1 +1 2 + 4 n=1 n2 4 Answer:
Fourier Series please answer no. (2) when p=2L=1 - cos nx dx = bn(TE) +277 f(x) sin nx dx (- /<x< 1 2) p=1 2. f(x) = = COS TEX 3. Find the Fourier series of the function below: f(x) k 2 1-k Simplification of Even and Odd Function:
The series Σ 1 np converges if and only if p < 1 Select one: O True O False